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H133_quiz3_key - Name EU Physics H133(Spring 2011 Quiz#3...

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Unformatted text preview: Name: EU Physics H133 (Spring, 2011): Quiz #3 Full credit 2 10 points Possibly useful relations: 27r h he f A f P \/2(mCQ)K Ezhfzjc thf-W cos0=%(e“9+e'19) isin0:%(elg—e’10) Consider the SG devices above. Of the electrons entering the last device, what fraction exit through the negative output of the SGZ device? (circle one) (a) 0 (b) cosz(6’/2) [email protected] (d) 1.0 (e) sin2(9/2) Explainyour response using QM rules. (1 pt. for correct answer, 1 pt. for correct explanation) \ «533% (“$0939 Nu“ m “lim— ‘VD S07, \5. “L37. Wt oxiin éfo‘teviflioc gem“ (“ng mgi‘k‘) '60 \—DD\ R gamma) NU. aw? ‘N \ke‘uhcot \‘3 V \ \a ' / i . . a e”) (m 319%,, 2. (3 pts.) iii the setup of SG devices shown in problem (1) above, what is always true about the state 3 vector of the quantons exiting through the positive output of the middle device? Circle all that apply! (a) This state vector is the same as that of the quantons entering the middle device. @This state vector has collapsed to the |+y) eigenvector. (c) Quantum mechanics leaves us uncertain about this state vector after the middle device has performed its measurement. (d) This state vector must be an energy eigenvector. Explain your responses (including the ones that you did not circle)! (1 pt. for correct answers, 2 pts. for correct explanations (0.5 pts. for each option) ) ‘ _ \ A a m was were $90 W W M“ “77 W Ml" W7 hi“ mm .1332 mm 50m ON ‘93? C“ 9 txol TXT‘WE (c) We keg“) 20c (name had“ ‘5 its? 'm 9)?)‘5 MQUWW bum minim disz, i US) “My ‘02 enigma?) QWNQCRC but \1 m1” MM is he pm 3. (2 pts.) Considering the (unrealistic) wavefunction shown below (assume it is zero everywhere outside the graph), if we do a measurement that locates the quanton, what is the probability of a result to the right of the origin (which is in the center)? Answer: 7 4. (5’ pts.) At time t : 0, each electron in a beam has the state vector |tb(0)) = w/1/3|+Z)+i\/2/31—Z>, where |+z) and |—z) are also eigenvectors of energy, with eigenvalues 00V and 71 eV, respectively. (1 pt.) If at t = 0 the beam passes through an SGx device, what fraction do you expect to exit the negative output? b. (1 pt) What is WU»? c. (1 pt.) If at t = (7r/2)h the beam passes through an 8G3: device, what fraction do you expect to exit the negative output? Show your work! N in ff ‘ V [I m \ v‘ 3 a \amztl'olr \Elll: Mme“ M 4 “D will) he’ll)“ New 4am 1 fi—igerflflv % bY‘L We» Cog} GAEQM We): ('19 liltcne ‘37,) C\§;¢ofix '\ \<»s<\1t 1h 2.5 , taxi”; W9” w , gm garniflflLigltwtfiiZ \e." r. i, w _ r i M 1‘1 if” 1 ‘- ~ ' D §\<w\<l1t=\1l§)7l :: K“) J, :7 3:33} :Lquyt lL ‘ ‘2. ...
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